Finite Group Databasebeta

← #11808003

Subgroups — #11808003

Order 1152.

893 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63870C211yesmaximal, characteristic
2#10592676C211yesmaximal, characteristic
3C3×#4976C212yesmaximal
4#10591360C211yesmaximal, characteristic
5#10591331C212yesmaximal
6#10591272C212yesmaximal
7#10591255C212yesmaximal
8#10591246C212yesmaximal
9#10591193C212yesmaximal
10#75993—32nomaximal
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×Dic3⋊C4C2212yes—
15C2×C3×Dic3⋊C4C2212yes—
16C2×C3×Dic3⋊C4C2212yes—
17C2×C3×C4×Dic3C2212yes—
18C2×#3724C2211yescharacteristic
19C2×#3724C2211yescharacteristic
20C2×#3724C2211yescharacteristic
21C2×#3724C2211yescharacteristic
22C2×Dic3⋊Dic3C2212yes—
23C2×Dic32C2212yes—
24#63870C418yescomplemented
25#63658C2212yes—
26#63658C2212yes—
27C3×C3⋊#95C2212yes—
28C3×C3⋊#95C2212yes—
29#63579C2212yes—
30#63579C2212yes—
31#63579C2212yes—
32#63579C2212yes—
33C2×#889—32no—
34C3×#389—32no—
35#4980—32no—
36#4978—32no—
37#4978—32no—
38#4977—32no—
39#4977—61no—
40#4976—32no—
41#4976D312yes—
42#4972—32no—
43#4933—32no—
44#4933—32no—
45#4655—32no—
46#4654—32no—
47#4652—32no—
48#4650—32no—
49C22×C32×C4C2312yes—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3C2312yes—
52C22×C3⋊Dic3C2311yescharacteristic
53C22×C3⋊Dic3C2311yescharacteristic
54C22×C3×Dic3C2312yes—
55C22×C3×Dic3C2312yes—
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2312yes—
58C32×C4⋊C4—41no—
59C4⋊(C3⋊Dic3)—41no—
60C4×C3⋊Dic3C2×C414yes—
61C3×Dic3⋊C4—42no—
62C3×Dic3⋊C4—42no—
63C3×Dic3⋊C4C2×C418yes—
64C3×C4×Dic3—42no—
65#3724—41no—
66#3724—41no—
67#3724C2×C414yes—
68#3724C2×C414yes—
69Dic3⋊Dic3C2×C418yes—
70Dic32—42no—
71#2382—91noSylow
72C2×C3×C4⋊C4—21no—
73C2×C3×C4⋊C4—32no—
74C2×C3×C4⋊C4—32no—
75C2×C3×C4⋊C4—32no—
76C2×C3×C4⋊C4C2×D312yes—
77C2×C3×C42—32no—
78C2×C4⋊Dic3—32no—
79C2×C4⋊Dic3—32no—
80C2×C4⋊Dic3—61no—
81C2×Dic3⋊C4—32no—
82C2×Dic3⋊C4—32no—
83C2×Dic3⋊C4—32no—
84C2×Dic3⋊C4—32no—
85C2×Dic3⋊C4—32no—
86C2×Dic3⋊C4C2×D312yes—
87C2×Dic3⋊C4C2×D312yes—
88C2×Dic3⋊C4C2×D312yes—
89C2×C4×Dic3—32no—
90C2×C4×Dic3—32no—
91C2×C4×Dic3—32no—
92C2×C4×Dic3—61no—
93C2×C4×Dic3C2×D312yes—
94#889—316no—
95C3×#95—32no—
96C3×#95—32no—
97C3⋊#95—32no—
98C3⋊#95—32no—
99C3⋊#95—32no—
100C3⋊#95—32no—
101C3⋊#95—32no—
102C3⋊#95—32no—
103C3⋊#95—32no—
104C3⋊#95—32no—
105C3⋊#95—32no—
106C3⋊#95—32no—
107C3⋊#95—32no—
108C3⋊#95—32no—
109C3⋊#95—62no—
110C3⋊#95—62no—
111C3⋊#95C2×D312yes—
112C3⋊#95C2×D312yes—
113C23×C32C2411yescharacteristic
114C2×C32×C4—21no—
115C2×C32×C4—21no—
116C2×C32×C4—22no—
117C2×C32×C4—22no—
118C2×C32×C4—22no—
119C2×C32×C4C22×C412yes—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3C22×C412yes—
128C2×C3⋊Dic3C22×C412yes—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3C22×C414yes—
140C2×C3×Dic3C22×C414yes—
141C2×#125—91no—
142#389—32no—
143#389—92no—
144#387—92no—
145#387—92no—
146#387—92no—
147#387—92no—
148#382—91no—
149#382—91no—
150C22×C3×C4—21no—
151C22×C3×C4—22no—
152C22×C3×C4—32no—
153C22×C3×C4—32no—
154C22×C3×C4—32no—
155C22×C3×C4—32no—
156C22×C3×C4C22×D312yes—
157C22×C3×C4C22×D312yes—
158C22×C3×C4C22×D312yes—
159C22×Dic3—32no—
160C22×Dic3—32no—
161C22×Dic3—32no—
162C22×Dic3—32no—
163C22×Dic3—61no—
164C22×Dic3—61no—
165C22×Dic3—62no—
166C22×Dic3C22×D312yes—
167C22×Dic3C22×D312yes—
168C22×Dic3C22×D312yes—
169C22×Dic3C22×D312yes—
170C3×C4⋊C4—38no—
171C3×C4⋊C4—42no—
172C3×C4⋊C4—42no—
173C3×C4⋊C4—122no—
174C3×C4⋊C4—122no—
175C3×C42—122no—
176C4⋊Dic3—38no—
177C4⋊Dic3—122no—
178C4⋊Dic3—122no—
179Dic3⋊C4—38no—
180Dic3⋊C4—38no—
181Dic3⋊C4—38no—
182Dic3⋊C4—42no—
183Dic3⋊C4—42no—
184Dic3⋊C4—122no—
185Dic3⋊C4—122no—
186Dic3⋊C4C4×D318yes—
187C4×Dic3—38no—
188C4×Dic3—42no—
189C4×Dic3—64no—
190C4×Dic3—122no—
191C4×Dic3—122no—
192C22×C32C23×C411yescharacteristic
193C22×C32H(5,𝔽2)11yescharacteristic
194C22×C32H(5,𝔽2)11yescharacteristic
195C22×C322−1+411yescharacteristic
196C22×C322−1+411yescharacteristic
197C22×C322−1+411yescharacteristic
198C22×C322−1+411yescharacteristic
199C32×C4—22no—
200C32×C4—42no—
201C3⋊Dic3—22no—
202C3⋊Dic3—22no—
203C3⋊Dic3—42no—
204C3×Dic3—24no—
205C3×Dic3—24no—
206C3×Dic3—42no—
207C3×Dic3—42no—
208#125—98no—
209C2×C4⋊C4—32no—
210C2×C4⋊C4—32no—
211C2×C4⋊C4—32no—
212C2×C4⋊C4—91no—
213C2×C4⋊C4—91no—
214C2×C4⋊C4—92no—
215C2×C4⋊C4—91no—
216C2×C4⋊C4—91no—
217C2×C4⋊C4—91no—
218C2×C4⋊C4D3211yescharacteristic
219C2×C42—32no—
220C2×C42—91no—
221C2×C42—92no—
222#95—32no—
223#95—32no—
224#95—92no—
225#95—92no—
226#95—92no—
227#95—92no—
228#95—92no—
229#95—92no—
230C23×C3—21no—
231C23×C3C23×D312yes—
232C2×C3×C4—22no—
233C2×C3×C4—22no—
234C2×C3×C4—22no—
235C2×C3×C4—22no—
236C2×C3×C4—22no—
237C2×C3×C4—22no—
238C2×C3×C4—22no—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—34no—
244C2×C3×C4—34no—
245C2×C3×C4—42no—
246C2×C3×C4—42no—
247C2×C3×C4—42no—
248C2×C3×C4—62no—
249C2×C3×C4—62no—
250C2×C3×C4—62no—
251C2×C3×C4—62no—
252C2×C3×C4—62no—
253C2×C3×C4—62no—
254C2×C3×C4—62no—
255C2×C3×C4—62no—
256C2×C3×C4—62no—
257C2×C3×C4—62no—
258C2×C3×C4C2×C4×D314yes—
259C2×Dic3—22no—
260C2×Dic3—22no—
261C2×Dic3—22no—
262C2×Dic3—22no—
263C2×Dic3—22no—
264C2×Dic3—22no—
265C2×Dic3—22no—
266C2×Dic3—22no—
267C2×Dic3—22no—
268C2×Dic3—22no—
269C2×Dic3—34no—
270C2×Dic3—34no—
271C2×Dic3—62no—
272C2×Dic3—62no—
273C2×Dic3—62no—
274C2×Dic3—62no—
275C2×Dic3—62no—
276C2×Dic3—62no—
277C2×Dic3—62no—
278C2×Dic3—62no—
279C2×Dic3—62no—
280C2×Dic3—62no—
281C2×Dic3—62no—
282C2×Dic3—62no—
283C2×Dic3—121no—
284C2×Dic3—121no—
285C2×Dic3—121no—
286C2×Dic3—121no—
287C2×Dic3—122no—
288C2×Dic3—122no—
289C2×Dic3—122no—
290C2×Dic3C2×C4×D314yes—
291C2×Dic3C2×C4×D314yes—
292C2×C32#51911yescharacteristic
293C2×C32#52011yescharacteristic
294C2×C32#52011yescharacteristic
295C2×C32#56211yescharacteristic
296C2×C32#56311yescharacteristic
297C2×C32#56311yescharacteristic
298C2×C32#56411yescharacteristic
299C22×C4—32no—
300C22×C4—32no—
301C22×C4—32no—
302C22×C4—32no—
303C22×C4—91no—
304C22×C4—91no—
305C22×C4—92no—
306C22×C4C2×D3212yes—
307C22×C4C2×D3211yescharacteristic
308C4⋊C4—38no—
309C4⋊C4—41no—
310C4⋊C4—94no—
311C4⋊C4—94no—
312C4⋊C4—98no—
313C4⋊C4—122no—
314C4⋊C4—122no—
315C4⋊C4—361no—
316C4⋊C4—361no—
317C4⋊C4—361no—
318C42—94no—
319C42—122no—
320C42—362no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3C22×C4×D312yes—
329C22×C3#100412yes—
330C22×C3#100412yes—
331C22×C3#100712yes—
332C22×C3#100712yes—
333C22×C3#101012yes—
334C22×C3#101012yes—
335C3×C4—24no—
336C3×C4—24no—
337C3×C4—42no—
338C3×C4—42no—
339C3×C4—64no—
340C3×C4—64no—
341C3×C4—82no—
342C3×C4—122no—
343C3×C4—122no—
344Dic3—24no—
345Dic3—24no—
346Dic3—42no—
347Dic3—42no—
348Dic3—64no—
349Dic3—64no—
350Dic3—122no—
351Dic3—122no—
352Dic3—122no—
353Dic3—122no—
354Dic3—242no—
355C32#238211yescharacteristic, complemented, Sylow
356C23C22×D3211yescharacteristic
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—34no—
363C2×C4—34no—
364C2×C4—62no—
365C2×C4—62no—
366C2×C4—62no—
367C2×C4—62no—
368C2×C4—62no—
369C2×C4—62no—
370C2×C4—62no—
371C2×C4—62no—
372C2×C4—62no—
373C2×C4—62no—
374C2×C4—92no—
375C2×C4—92no—
376C2×C4—181no—
377C2×C4—181no—
378C2×C4—181no—
379C2×C4—181no—
380C2×C4—182no—
381C2×C4—182no—
382C2×C4—182no—
383C2×C4C4×D3212yes—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3#550412yes—
392C2×C3#554612yes—
393C2×C3#557212yes—
394C2×C3#562112yes—
395C2×C3#564612yes—
396C2×C3C3⋊#56412yes—
397C2×C3#573512yes—
398C22#6429811yescharacteristic
399C22C2×C4×D3211yescharacteristic
400C22#6430911yescharacteristic
401C22#6431311yescharacteristic
402C22#6431611yescharacteristic
403C22#6431611yescharacteristic
404C22#6433011yescharacteristic
405C4—22no—
406C4—42no—
407C4—64no—
408C4—64no—
409C4—122no—
410C4—122no—
411C4—182no—
412C4—182no—
413C4—362no—
414C3—21no—
415C3#7599312yescomplemented
416C2#1059434711yescharacteristic
417C2#1059435411yescharacteristic
418C2#1059450911yescharacteristic
419C2#1059458911yescharacteristic
420C2#1059487611yescharacteristic
421C2#1059521311yescharacteristic
422C2#1059535211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2382
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
24. #63870C4semidirect
355. C32#2382semidirect
415. C3#75993semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#638702
#105926762
C3×#49762
#105913602
#105913312
#105912722
#105912552
#105912462
#105911932
#759933